Summary: Lower Bounds for Distributed Coin-Flipping and
Randomized Consensus
James Aspnes y
February 2, 1998
Abstract
We examine a class of collective coin- ipping games that arises from
randomized distributed algorithms with halting failures. In these games,
a sequence of local coin ips is generated, which must be combined to
form a single global coin ip. An adversary monitors the game and may
attempt to bias its outcome by hiding the result of up to t local coin
ips. We show that to guarantee at most constant bias, (t2
) local coins
are needed, even if (a) the local coins can have arbitrary distributions
and ranges, (b) the adversary is required to decide immediately whether
to hide or reveal each local coin, and (c) the game can detect which
local coins have been hidden. If the adversary is permitted to control the
outcome of the coin except for cases whose probability is polynomial in t,
(t2
= log2
t) local coins are needed. Combining this fact with an extended